Dynamics of spinor condensates near point-group symmetric ground states

The mean-field ground state of spin-S BEC's often exhibits a high degree of symmetry, which only becomes apparent when considering the 2S reciprocal spin-states: coherent spin-states orthogonal to the ground state. Our presentation will concentrate on a description of the dynamics of spinor-condensates using these reciprocal states. First, we will present the resulting hydrodynamic Euler equations, which generalize Mermin-Ho relations to higher spin. Second, we will use the reciprocal states and their hidden point-group symmetry to construct the Goldstone and optical spin-wave modes of the spinor condensates. Finally, we will present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field.